[Efficacité amortissante du schéma explicite dissipatif de Tchamwa–Wielgosz pour des chargements impulsionnels]
To deal with dynamic and wave propagation problems, dissipative methods are often used to reduce the effects of the spurious oscillations induced by the spatial and time discretization procedures. Among the many dissipative methods available, the Tchamwa–Wielgosz (TW) explicit scheme is particularly useful because it damps out the spurious oscillations occurring in the highest frequency domain. The theoretical study performed here shows that the TW scheme is decentered to the right, and that the damping can be attributed to a nodal displacement perturbation. The FEM study carried out using instantaneous 1-D and 3-D compression loads shows that it is useful to display the damping versus the number of time steps in order to obtain a constant damping efficiency whatever the size of element used for the regular meshing. A study on the responses obtained with irregular meshes shows that the TW scheme is only slightly sensitive to the spatial discretization procedure used.
Dans le cadre de problèmes de dynamique ou de propagation d'ondes, l'utilisation d'une méthode dissipative est souvent nécessaire pour réduire les oscillations parasites provenant des discrétisations spatiales et temporelles. Parmi les nombreuses méthodes existantes, le schéma explicite dissipatif de Tchamwa–Wielgosz amortit ces oscillations en ciblant son amortissement sur l'énergie des hautes fréquences. Une étude théorique montre ici le décentrage à droite de ce schéma et interprète son amortissement comme une perturbation des déplacements nodaux. L'étude FEM sur des cas de compression impulsionnelle 1-D et 3-D montre l'utilité d'afficher l'amortissement en fonction du nombre de pas de temps et permet d'obtenir une efficacité amortissante constante quelque soit la taille de l'élément utilisé dans le maillage régulier. L'étude de la réponse obtenue pour des maillages irréguliers montre la légère sensibilité de l'amortissement du schéma de TW à la discrétisation spatiale utilisée.
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Mots-clés : Systèmes dynamiques, Algorithme d'intégration temporelle explicite et dissipatif, Schéma de Tchamwa–Wielgosz
Laurent Mahéo 1, 2 ; Vincent Grolleau 2, 3 ; Gérard Rio 2
@article{CRMECA_2009__337_11-12_722_0,
author = {Laurent Mah\'eo and Vincent Grolleau and G\'erard Rio},
title = {Damping efficiency of the {Tchamwa{\textendash}Wielgosz} explicit dissipative scheme under instantaneous loading conditions},
journal = {Comptes Rendus. M\'ecanique},
pages = {722--732},
publisher = {Elsevier},
volume = {337},
number = {11-12},
year = {2009},
doi = {10.1016/j.crme.2009.10.005},
language = {en},
}
TY - JOUR AU - Laurent Mahéo AU - Vincent Grolleau AU - Gérard Rio TI - Damping efficiency of the Tchamwa–Wielgosz explicit dissipative scheme under instantaneous loading conditions JO - Comptes Rendus. Mécanique PY - 2009 SP - 722 EP - 732 VL - 337 IS - 11-12 PB - Elsevier DO - 10.1016/j.crme.2009.10.005 LA - en ID - CRMECA_2009__337_11-12_722_0 ER -
%0 Journal Article %A Laurent Mahéo %A Vincent Grolleau %A Gérard Rio %T Damping efficiency of the Tchamwa–Wielgosz explicit dissipative scheme under instantaneous loading conditions %J Comptes Rendus. Mécanique %D 2009 %P 722-732 %V 337 %N 11-12 %I Elsevier %R 10.1016/j.crme.2009.10.005 %G en %F CRMECA_2009__337_11-12_722_0
Laurent Mahéo; Vincent Grolleau; Gérard Rio. Damping efficiency of the Tchamwa–Wielgosz explicit dissipative scheme under instantaneous loading conditions. Comptes Rendus. Mécanique, Volume 337 (2009) no. 11-12, pp. 722-732. doi : 10.1016/j.crme.2009.10.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.10.005/
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